A case study of theorem proving by the Knuth-Bendix method: Discovering that x 3 = x implies ring commutativity

2006 ◽  
pp. 248-258 ◽  
Author(s):  
Mark E. Stickel
Keyword(s):  
Theorem Proving

Automatic Theorem Proving for Natural Logic: a Case Study on Textual Entailment

2018 ◽  
Vol 22 (1) ◽  
Author(s):  
José de Jesús Lavalle Martínez ◽  
Manuel Montes y Gómez ◽  
Héctor Jiménez Salazar ◽  
Luis Villaseñor Pineda ◽  
Beatriz Beltrán Martínez
Keyword(s):  
Theorem Proving ◽  
Automatic Theorem Proving ◽  
Natural Logic ◽  
Textual Entailment ◽  
Automatic Theorem

scholarly journals Bayesian Optimisation for Heuristic Configuration in Automated Theorem Proving

10.29007/q91g ◽  
2020 ◽  
Author(s):  
Agnieszka Słowik ◽  
Chaitanya Mangla ◽  
Mateja Jamnik ◽  
Sean Holden ◽  
Lawrence Paulson
Keyword(s):  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Probabilistic Framework ◽  
Selection Algorithm ◽  
Formal Proofs ◽  
Proof Search ◽  
Minimum Number ◽  
Selection Algorithms

Modern theorem provers such as Vampire utilise premise selection algorithms to control the proof search explosion. Premise selection heuristics often employ an array of continuous and discrete parameters. The quality of recommended premises varies depending on the parameter assignment. In this work, we introduce a principled probabilistic framework for optimisation of a premise selection algorithm. We present results using Sumo Inference Engine (SInE) and the Archive of Formal Proofs (AFP) as a case study. Our approach can be used to optimise heuristics on large theories in minimum number of steps.

scholarly journals Deadlock and starvation free reentrant readers–writers: A case study combining model checking with theorem proving

2011 ◽  
Vol 76 (2) ◽  
pp. 82-99 ◽  
Author(s):  
Bernard van Gastel ◽  
Leonard Lensink ◽  
Sjaak Smetsers ◽  
Marko van Eekelen
Keyword(s):  
Model Checking ◽  
Theorem Proving

Description Logic for Product Information Models

2008 ◽  
Author(s):  
X. Fiorentini ◽  
S. Rachuri ◽  
M. Mahesh ◽  
S. Fenves ◽  
Ram D. Sriram
Keyword(s):  
Theorem Proving ◽  
Description Logic ◽  
Product Information ◽  
Rule Engine ◽  
Product Model ◽  
Domain Experts ◽  
Information Models ◽  
Structured Knowledge ◽  
Product Assembly

The languages and logical formalisms developed by information scientists and logicians concentrate on the theory of languages and logical theorem proving. These languages, when used by domain experts to represent their domain of discourse, most often have issues related to the level of expressiveness of the languages and need specific extensions. In this paper we analyze the levels of logical formalisms and expressivity requirements for the development of ontologies for manufacturing products. We first discuss why the representation of a product model is inherently complex and prone to inconsistencies. We then explore how these issues can be overcome through a structured knowledge representation model. We report our evaluation of OWL-DL in terms of expressivity and of the use of SWRL for representing domainspecific rules. We present a case study of product assembly to document this evaluation and further show how the OWL-DL reasoner together with the rule engine can enable reasoning of the product ontology.

Situating the Debate on “Geometrical Algebra” within the Framework of Premodern Algebra

2016 ◽  
Vol 29 (2) ◽  
pp. 129-150 ◽  
Author(s):  
Michalis Sialaros ◽  
Jean Christianidis
Keyword(s):  
Comparative Analysis ◽  
Problem Solving ◽  
Theorem Proving ◽  
Algebraic Reasoning ◽  
Numerical Problem ◽  
Controversial Topic ◽  
Methodological Approaches ◽  
Greek Mathematics ◽  
Geometrical Algebra

ArgumentThe aim of this paper is to employ the newly contextualized historiographical category of “premodern algebra” in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on “geometrical algebra.” Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related toElem.II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called “semi-algebraic” alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing “premodern algebra,” and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

scholarly journals Bayesian Optimisation for Premise Selection in Automated Theorem Proving (Student Abstract)

2020 ◽  
Vol 34 (10) ◽  
pp. 13919-13920
Author(s):  
Agnieszka Słowik ◽  
Chaitanya Mangla ◽  
Mateja Jamnik ◽  
Sean B. Holden ◽  
Lawrence C. Paulson
Keyword(s):  
Parameter Space ◽  
Theorem Proving ◽  
Automated Theorem Proving ◽  
Search Space ◽  
Large Set ◽  
Probabilistic Framework ◽  
Formal Proofs ◽  
Dimensional Parameter ◽  
Theorem Provers

Modern theorem provers utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probabilistic framework for heuristic optimisation in theorem provers. We present results using a heuristic for premise selection and the Archive of Formal Proofs (AFP) as a case study.

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